A sample of air weighing 1.18g occupies
Question: A sample of air weighing $1.18 \mathrm{~g}$ occupies $1.0 \times 10^{3} \mathrm{~cm}^{3}$ when kept at $300 \mathrm{k}$ and $1.0 \times 10^{5} \mathrm{~Pa}$. When $2.0$ cal of heat is added to it at constant volume, its temperature increase the temperature of air by $1^{\circ} \mathrm{C} t$ constant pressure, if the temperature of air by $1^{\circ} \mathrm{C}$ at constant pressure, if the mechanical equivalent of heat is $4.2 \times 10^{7} \mathrm{erg} / \mathrm{cal}$. Assume that air ...
Read More →The ratio of the molar heat capacities of an ideal gas
Question: The ratio of the molar heat capacities of an ideal gas is $C_{p} / C_{v}=7 / 6$. Calculate the change in internal energy of $1.0$ mol of the gas when its temperature is raised by $50 \mathrm{~K}$ (a) keeping the pressure constant, (b) keeping the volume constant and (c) adiabatically. Solution:...
Read More →The specific heat capacities of hydrogen at constant volume
Question: The specific heat capacities of hydrogen at constant volume and at constant pressure are $2.4 \mathrm{cal} / \mathrm{g}-{ }^{\circ} \mathrm{C}$ and $3.4 \mathrm{cal} / \mathrm{g}-{ }^{\circ} \mathrm{C}$ respectively, The molecular weight of hydrogen is $2 \mathrm{~g} / \mathrm{mol}$ and the gas constant $R$ $=8.3 \times 10^{7} \mathrm{erg} / \mathrm{mol}{ }^{\circ} \mathrm{c}$. Calculate the value of $\mathrm{J}$. Solution:...
Read More →Figure. Shows a cylindrical container containing oxygen
Question: Figure. Shows a cylindrical container containing oxygen $(\gamma=1.4)$ and closed by aa $50 \mathrm{~kg}$ frictionless piston. The area of cross section is $100 \mathrm{~cm}^{3}$, atmospheric pressure is $100 \mathrm{kPa}$ and $\mathrm{g}$ is $10 \mathrm{~m} / \mathrm{s}^{2}$. The cylinder is slowly heated for some time. Find the amount of heat supplied to the gas if the piston moves out through a distance of $20 \mathrm{~cm}$. Solution:...
Read More →5g of a gas is contained in a rigid container and
Question: $5 \mathrm{~g}$ of a gas is contained in a rigid container and is heated from $15^{\circ} \mathrm{C}$ to $25^{\circ} \mathrm{C} .$ Specific heat capacity of the gas at constant volume is $0.172 \mathrm{cal} / \mathrm{g}-{ }^{\circ} \mathrm{C}$ and the mechanical equivalent of heat is $4.2 \mathrm{~J} / \mathrm{cal}$. Calculate the change in the internal energy of the gas. Solution:...
Read More →A vessel containing one mole of a monatomic ideal gas
Question: A vessel containing one mole of a monatomic ideal gas (molecular weight $=20 \mathrm{~g} / \mathrm{mol}$ ) is moving on a floor at a speed of $50 \mathrm{~m} / \mathrm{s}$. The vessel is stopped suddenly. Assuming that the mechanical energy lost has gone into the internal energy of the gas, find the rise in its temperature. Solution:...
Read More →An adiabatic vessel of total volume V is divided into two equal parts
Question: An adiabatic vessel of total volume $\mathrm{V}$ is divided into two equal parts by a conducting separator. The separator is fixed in this position. The part on the contains one mole of an ideal gas $(U=1.5 n R T)$ and the part on the right contains two moles of the same gas. Initially, the pressure on each side is p. The system is left for sufficient time so that a steady state is reached. Find (a) the work done by the gas in the left part during the process, (b) the temperature on th...
Read More →Figure (26-E11) shows a cylindrical tube of volume V
Question: Figure (26-E11) shows a cylindrical tube of volume $\mathrm{V}$ with adiabatic walls containing an ideal gas. The internal energy of this ideal gas is given by $1.5 \mathrm{nRT}$. The tube is divided into two equal parts by a fixed diathermic wall. Initially, the pressure and the temperature are $\mathrm{p}_{1}, \mathrm{~T}_{1}$ on the left and $\mathrm{p}_{2}, \mathrm{~T}_{2}$ on the right. The system is left for sufficient time so that the temperature becomes equal on the two sides. ...
Read More →Calculate the increase in the internal energy of
Question: Calculate the increase in the internal energy of $10 \mathrm{~g}$ of water when it is heated from $0^{\circ} \mathrm{C}$ to $100^{\circ} \mathrm{C}$ and converted into steam at $100 \mathrm{kPa}$. The density of steam $=0.6 \mathrm{~kg} / \mathrm{m}^{3}$. Specific heat capacity of water $=4200 \mathrm{~J} / \mathrm{kg}^{-}{ }^{\circ} \mathrm{C}$ and the latent heat of vaporization of water $=2.5 \times 10^{6} \mathrm{~J} / \mathrm{kg}$. Solution:...
Read More →Find the change in the internal energy of 2kg
Question: Find the change in the internal energy of $2 \mathrm{~kg}$ of water as it is heated from $0^{\circ} \mathrm{C}$ to $4^{\circ} \mathrm{C}$. The specific heat capacity of water is $4200 \mathrm{~J} / \mathrm{kg}-\mathrm{K}$ and its densities at $0^{\circ} \mathrm{C}$ to $4^{\circ} \mathrm{C}$ are $999.9 \mathrm{~kg} / \mathrm{m}^{3}$ and $1000 \mathrm{~kg} / \mathrm{m}^{3}$ respectively. Atmospheric pressure $=10^{6} \mathrm{~Pa}$. Solution:...
Read More →Figure (26-E10) shows the variation in the internal energy U
Question: Figure (26-E10) shows the variation in the internal energy $U$ with the volume $\mathrm{V}$ of $2.0$ mole of an ideal gas in a cyclic process abcda. The temperature of the gas at $b$ and c are $500 \mathrm{k}$ and $300 \mathrm{k}$ respectively, Calculate the heat absorbed by the gas during the process. Solution:...
Read More →Consider the cyclic process ABCA,
Question: Consider the cyclic process ABCA, shown in figure (26-E9), performed on a sample of $2.0$ mole of an ideal gas. A total of $1200 \mathrm{~J}$ of heat is withdrawn from the sample in the process. Find the work done by the gas during the part $B C$. Solution:...
Read More →A gas is initially at a pressure of 100kPa
Question: A gas is initially at a pressure of $100 \mathrm{kPa}$ and its volume is $2.0 \mathrm{~m}^{3}$. Its pressure is kept constant and the volume is changed from $2.0 \mathrm{~m}^{3}$ to $2.5 \mathrm{~m}^{3}$. Its volume is now kept constant and the pressure is increased from $100 \mathrm{kPa}$ to $200 \mathrm{kPa}$. The gas is brought back to its volume. (a) Whether the heat is supplied to or extracted from the gas in the complete cycle? (b) How much heat was supplied or extracted? Solutio...
Read More →A gas is enclosed in a cylindrical vessel fitted
Question: A gas is enclosed in a cylindrical vessel fitted with a frictionless piston. The gas is slowly heated for some time. During the process, $10 \mathrm{~J}$ of heat is supplied and the piston is found to move out $10 \mathrm{~cm}$. Find the increase in the internal energy of the gas. The area of cross-section of the cylinder $=4 \mathrm{~cm}^{2}$ and the atmospheric pressure $=100 \mathrm{kPa}$. Solution:...
Read More →The internal energy of a gas is given by
Question: The internal energy of a gas is given by $\mathrm{U}=1.5 \mathrm{pV}$. It expands from $100 \mathrm{~cm}^{3}$ to $200 \mathrm{~cm}^{3}$ against a constant pressure of $1.0 \times 10^{6} \mathrm{~Pa}$ Calculate the heat absorbed by the gas in the process. Solution:...
Read More →A gas is taken along the path A B as shown in figure (26-E8).
Question: A gas is taken along the path $A B$ as shown in figure (26-E8). If 70 cal of heat is extracted from the gas in the process, calculate the change in the internal energy of the system. Solution:...
Read More →A substance is taken through the process abc as shown in figure (26-E7).
Question: A substance is taken through the process abc as shown in figure (26-E7). If the internal energy of the substance increases by $5000 \mathrm{~J}$ and a heat of $2625 \mathrm{cal}$ is given to the system, calculate the value of J. Solution:...
Read More →A gas is taken through a cyclic process ABCA as shown in figure
Question: A gas is taken through a cyclic process ABCA as shown in figure, (26-E6). If $2.4 \mathrm{cl}$ of heat is given in the process, what is the value of $\mathrm{J}$ ? Solution:...
Read More →Calculate the heat absorbed by a system in going through
Question: Calculate the heat absorbed by a system in going through the cyclic process shown in figure (26-E5). Solution:...
Read More →50cal of heat should be supplied to take a system from
Question: $50 \mathrm{cal}$ of heat should be supplied to take a system from the state $A$ to the state $B$ through the path $A C B$ as shown in figure (26-E4). Find the quantity of heat to be supplied to take it from $A$ to $B$ via ADB. Solution:...
Read More →When a system is taken through the process abc shown in figure (26-E3),
Question: When a system is taken through the process abc shown in figure (26-E3), $80 \mathrm{~J}$ of heat is absorbed by the system and $30 \mathrm{~J}$ of work is done by it. If the system does $10 \mathrm{~J}$ of work during the process adc, how much heat flows into it during the process? Solution:...
Read More →Figure (26-E2) shows three paths through which a gas can be taken
Question: Figure (26-E2) shows three paths through which a gas can be taken from the state A to the B. Calculate the work done by the gas in each of the three paths. Solution:...
Read More →An ideal gas is taken from an initial state i
Question: An ideal gas is taken from an initial state $i$ to a final state $f$ in such a way that the ratio of the pressure to the absolute temperature remains constant. What will be the work done by the gas? Solution:...
Read More →The pressure of a gas changes linearly with volume from
Question: The pressure of a gas changes linearly with volume from $10 \mathrm{kPa}, 200 \mathrm{cc}$ to $50 \mathrm{kPa}, 50 \mathrm{cc}$. (a) Calculate the work done by the gas. (b) If no heat is supplied or extracted from the gas, what is the change in the internal energy of the gas? Solution:...
Read More →Calculate the change in internal energy of a gas kept
Question: Calculate the change in internal energy of a gas kept in a rigid container when $100 \mathrm{~J}$ of heat is supplied to it. Solution:...
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