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. \(5~\text J\)

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

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. \(1 . 8 \times10^{2}~\text J\)$\mathrm{}$

For the isothermal reversible expansion of an ideal gas: 

1. $∆\mathrm{H}>0<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>∆\mathrm{U}=0$

2. $∆\mathrm{H}>0<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>∆\mathrm{U}<0$

3. $∆\mathrm{H}=0<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>∆\mathrm{U}=0$

4. $∆\mathrm{H}=0<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>∆\mathrm{U}>0$

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. \(25~ \mathrm{J}\)

A refrigerator works between $4°\mathrm{C}$ and $30°\mathrm{C}$. It is required to remove 600 calories of heat every second in order to keep the temperature of the refrigerated space constant. The power is $(\mathrm{Take}<mspace\; width="1em"></mspace>1<mspace\; width="1em"></mspace>\mathrm{cal}=4.2<mspace\; width="1em"></mspace>\mathrm{Joules})$

1. 2.365 W

2. 23.65 W

3. 236.5 W

4. 2365 W

\(1~\text g\) 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. \(2256~\text J\) 

The standard enthalpy of vaporization ${∆}_{\mathrm{vap}}{\mathrm{H}}^{\mathrm{o}}$ for water at 100 ^oC is 40.66 kJ mol^–1. The internal energy of vaporization of water at 100 ^oC (in kJ mol^–1) is: 
(Assume water vapour behaves like an ideal gas.)

1. +37.56

2. –43.76

3. +43.76

4. +40.66