The degree of freedom per molecule for a gas on average is 8. If the gas performs 100 J of work when it expands under constant pressure, then the amount of heat absorbed by the gas is:
1. 500 J
2. 600 J
3. 20 J
4. 400 J

For the isothermal reversible expansion of an ideal gas: 

1. $∆\mathrm{H}>0 \mathrm{and} ∆\mathrm{U}=0$

2. $∆\mathrm{H}>0 \mathrm{and} ∆\mathrm{U}<0$

3. $∆\mathrm{H}=0 \mathrm{and} ∆\mathrm{U}=0$

4. $∆\mathrm{H}=0 \mathrm{and} ∆\mathrm{U}>0$

\(1~\text g\) of water of volume \(1~\text{cm}^3\) at \(100^\circ \text{C}\) is converted into steam at the same temperature under normal atmospheric pressure \(\approx 1\times10^{5}~\text{Pa}.\) The volume of  steam formed equals \(1671~\text{cm}^3.\) If the specific latent heat of vaporization of water is \(2256~\text{J/g},\) the change in internal energy is:
1. \(2423~\text J\) 
2. \(2089~\text J\) 
3. \(167~\text J\) 
4. \(2256~\text J\) 

In the \((P\text-V)\) diagram shown, the gas does \(5~\text J\) of work in the isothermal process \(ab\) and \(4~\text J\) in the adiabatic process \(bc.\) What will be the change in internal energy of the gas in the straight path from \(c\) to \(a?\) 

             
1. \(9~\text J\)
2. \(1~\text J\)
3. \(4~\text J\)
4. \(5~\text J\)

1 kg of gas does 20 kJ of work and receives 16 kJ of heat when it is expanded between two states. The second kind of expansion can be found between the same initial and final states, which requires a heat input of 9 kJ. The work done by the gas in the second expansion will be:

The pressure of a monoatomic gas increases linearly from $\mathrm{}$\(4\times 10^5~\text{N/m}^2\) to $\mathrm{}$\(8\times 10^5~\text{N/m}^2\) when its volume increases from \(0.2 ~\text m^3\) to \(0.5 ~\text m^3.\) The work done by the gas is:
1. \(2 . 8 \times10^{5}~\text J\)
2. \(1 . 8 \times10^{6}~\text J\)
3. \(1 . 8 \times10^{5}~\text J\)
4. \(1 . 8 \times10^{2}~\text J\)$\mathrm{}$

A monoatomic ideal gas, initially at temperature \(T_1\), is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature \(T_2\) by releasing the piston suddenly. If \(L_1\) and \(L_2\) are the lengths of the gas column before and after expansion, respectively, then \(\frac{T_1}{T_2}\) is given by:
1. \(\left(\frac{L_1}{L_2}\right)^{\frac{2}{3}}\)
2. \(\frac{L_1}{L_2}\)
3. \(\frac{L_2}{L_1}\)
4. \(\left(\frac{L_2}{L_1}\right)^{\frac{2}{3}}\)

The initial pressure and volume of a gas are \(P\) and \(V\), respectively. First, it is expanded isothermally to volume \(4V\) and then compressed adiabatically to volume \(V\). The final pressure of the gas will be: [Given: \(\gamma = 1.5\)]

Under the isothermal condition, a gas at \(300 \mathrm{~K}\) expands from \(0.1 \mathrm{~L}\) to \(0.25 \mathrm{~L}\) against a constant external pressure of 2 bar. The work done by the gas is:
1. \(30 ~\mathrm {J} \)
2. \(-30 ~\mathrm{J} \)
3. \(5~ \mathrm{kJ}\)
4. \(25~ \mathrm{J}\)