During adiabatic expansion, the volume of air increases by 4%. The percentage decrease in the pressure will be

• 3.2 %

• 5.6 %

• 1.5 %

• 4.8 %

202.

Consider two containers P and Q containing identical gases at same temperature, pressure and volume. The gas in container P is compressed to half of its original volume isothermally while the gas in container Q is compressed to half of its original value adibatically. The ratio of final pressure of gas is

• $2^{\mathrm{\gamma }-1}$

• ${\left(\frac{1}{2}\right)}^{\mathrm{\gamma }-1}$

• ${\left(\frac{1}{1 - \mathrm{\gamma }}\right)}^2$

• ${\left(\frac{1}{\mathrm{\gamma } - 1}\right)}^2$

A refrigerator is driven by 1000 W electric motor having an efficiency of 60%. The refrigerator is considered as a reversible heat engine operating between 273 K and 303 K. Time required by it to freeze 32.5 kg of water at 0°C is. (Given, latent heat of fusion of ice = 336 × 10³ J-kg^-1 and heat lost may be neglected).

• 53 min 20 s

• 33 min 20 s

• 48 min 40 s

• 28 min 32 s

Work of 146 kJ is performed in order to compress one kilo mole of a gas adiabatically and in this process the temperature ofthe gas increases by 7° C. The gas is (R = 8.3 J mol^-1 K^-1 )

• diatomic

• triatomic

• a mixture of monoatomic and diatomic

• monoatomic

Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases to V^q , where V is the volume of the gas. The value of q is $\left(\mathrm{where} \mathrm{\gamma } = \frac{{\mathrm{C}}_{\mathrm{p}}}{{\mathrm{C}}_{\mathrm{V}}}\right)$

• $\frac{3\mathrm{\gamma } + 5}{6}$

• $\frac{3\mathrm{\gamma } - 5}{6}$

• $\frac{\mathrm{\gamma } + 1}{2}$

• $\frac{\mathrm{\gamma } - 1}{2}$

An ideal heat engine exhausting heat at 27° C is to have 25% efficiency. It must take heat at

• 127 °C

• 227° C

•  327° C

• None of these

Two spherical soap bubbles of radii r₁ and r₂ in vacuum combine under isothermal conditions. The resulting bubble has a radius equal to

• $\frac{{\mathrm{r}}_1 + {\mathrm{r}}_2}{2}$

• $\frac{{\mathrm{r}}_1{\mathrm{r}}_2}{{\mathrm{r}}_1 + {\mathrm{r}}_2}$

• $\sqrt{{\mathrm{r}}_1{\mathrm{r}}_2}$

• $\sqrt{{{\mathrm{r}}_1}^2 + {{\mathrm{r}}_2}^2 }$

The pressure and density of a diatomic gas $\left(\mathrm{\gamma } = \frac{7}{5}\right)$ change adiabatically from (P₁ , ρ₁) to (P₂ , ρ₂) . If $\frac{{\mathrm{\rho }}_2}{{\mathrm{\rho }}_1} = 32$ , then $\frac{{\mathrm{P}}_2}{{\mathrm{P}}_1}$ should be

• 16

• 32

• 64

• 128

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, then final temperature of the gas will be

• (T − 4) K

• (T + 4) K

• (T − 2.4)K

• (T + 2.4) K

According to first law of thermodynamics

• energy is conserved

• mass is conserved

• heat is constant in isothermal process

• heat neither enters nor leaves system