Which is the correct statement ?

(1) For an isothermal change PV = constant

(2) In an isothermal process the change in internal energy must be equal to the work done

(3) For an adiabatic change $\frac{P_2}{P_1}={\left(\frac{{\displaystyle V_2}}{{\displaystyle V_1}}\right)}^{\gamma }$, where γ is the ratio of specific heats

(4) In an adiabatic process work done must be equal to the heat entering the system

During the adiabatic expansion of 2 moles of a gas, the internal energy of the gas is found to decrease by 2 joules, the work done during the process by the gas will be equal to -

(1) 1 J

(2) –1 J

(3) 2 J

(4) – 2 J

If $\gamma$ denotes the ratio of two specific heats of a gas, the ratio of slopes of adiabatic and isothermal PV curves at their point of intersection is 

(1) $\frac{1}{\gamma }$

(2) $\gamma$

(3) $\gamma -1$

(4) $\gamma +1$

Air in a cylinder is suddenly compressed by a piston, which is then maintained at the same position. With the passage of time 

The adiabatic Bulk modulus of a perfect gas at pressure P is given by 

(1) P

(2) 2P

(3) P/2

(4) γ P

An adiabatic process occurs at constant 

(1) Temperature

(2) Pressure

(3) Heat

(4) Temperature and pressure

For adiabatic processes $\left(\gamma =\frac{C_p}{C_v}\right)$ 

(1) $P^{\gamma }V$ = constant

(2) $T^{\gamma }V$ = constant

(3) $T{V}^{\gamma -1}$ = constant

(4) $T{V}^{\gamma }$ = constant

An ideal gas is expanded adiabatically at an initial temperature of \(300~\text{K}\) so that its volume is doubled. The final temperature of the hydrogen gas is: \((\gamma = 1.40)~\left[2^{0.4}= 1.3\right]\)
1. \(230.76~\text{K}\)
2. \(500.30~\text{K}\)
3. \(454.76~\text{K}\)
4. \(-47~^{\circ}\text{C}\)

In an adiabatic expansion of a gas, if the initial and final temperatures are \(T_1\) and \(T_2\), respectively, then the change in internal energy of the gas is:
1. \(\frac{nR}{\gamma-1}(T_2-T_1)\)
2. \(\frac{nR}{\gamma-1}(T_1-T_2)\)
3. \(nR ~(T_1-T_2)\)
4. Zero