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

Helium at 27°C has a volume of 8 litres. It is suddenly compressed to a volume of 1 litre. The temperature of the gas will be [γ = 5/3] 

(1) 108°C

(2) 9327°C

(3) 1200°C

(4) 927°C

A cycle tyre bursts suddenly. This represents an 

(1) Isothermal process

(2) Isobaric process

(3) Isochoric process

(4) Adiabatic process

One mole of helium is adiabatically expanded from its initial state $(P_i,V_i,T_i)$ to its final state $(P_f,V_f,T_f)$. The decrease in the internal energy associated with this expansion is equal to

(1) $C_V(T_i-T_f)$

(2) $C_P(T_i-T_f)$

(3) $\frac{1}{2}(C_P+C_V)(Ti-T_f)$

(4) $(C_P-C_V)(T_i-T_f)$

A diatomic gas initially at 18°C is compressed adiabatically to one-eighth of its original volume. The temperature after compression will be 

(1) 10°C

(2) 887°C

(3) 668 K

(4) 144°C

One mole of an ideal gas at an initial temperature of T K does 6R joules of work adiabatically. If the ratio of specific heats of this gas at constant pressure and at constant volume is 5/3, the final temperature of the gas will be:

The volume of a gas is reduced adiabatically to $\frac{1}{4}$ of its volume at 27°C, if the value of γ = 1.4, then the new temperature will be - 

(1) 350 × 4^0.4 K

(2) 300 × 4^0.4 K

(3) 150 × 4^0.4 K

(4) None of these

For an adiabatic expansion of a perfect gas, the value of $\frac{\Delta P}{P}$ is equal to 

(1) $-\sqrt{\gamma }\frac{\Delta V}{V}$

(2) $-\frac{\Delta V}{V}$

(3) $-\gamma \frac{\Delta V}{V}$

(4) $-{\gamma }^2\frac{\Delta V}{V}$