2 Marks Questions

Question 12 Marks

Consider a P-V diagram in which the path followed by one mole of perfect gas in a cylindrical container is shown in Fig.

What is the ratio of temperature $\frac{\text{T}_1}{\text{T}_2},\text{if}\text{V}_2=2\text{V}_1?$

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Question 22 Marks

If the co-efficient of performance of a refrigerator is 5 and operates at the room temperature (27°C), find the temperature inside the refrigerator.

Answer

We know, $\beta=\frac{\text{T}_{2}}{\text{T}_{1}-\text{T}_{2}}$ $\big(\beta={5},\text{ T}_{1}=27+273=300\text{K}\big)$$5=\frac{\text{T}_{2}}{300-\text{T}_{2}}\Rightarrow\text{T}_{2}=1500-5\text{T}_{2}$
$\text{T}_{2}+5\text{T}_{2}=1500\Rightarrow6\text{T}_{2}=1500$
$\text{T}_{2}=\frac{1500}{6}=250\text{K}=250-273=-23^\circ\text{C}.$

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Question 32 Marks

Consider a P-V diagram in which the path followed by one mole of perfect gas in a cylindrical container is shown in Fig.

Find the work done when the gas is taken from state 1 to state 2.

Answer

$\therefore\text{PV}^\frac{1}{2}= $ constant = K (given) or Work done for process from 1 to 2
$\text{WD}=\int\limits^{\text{v}_{2}}_{\text{v}_{1}}\text{P}.\text{dV}=\int\limits^{\text{v}_{2}}_{\text{v}_{1}}\frac{\text{K}}{\text{V}^\frac{1}{2}}\text{dV}=\text{K}\int\limits^{\text{v}_{2}}_{\text{v}_{1}}\text{V}^{-\big(\frac{1}{2}\big)\text{dV}}$$$
$\text{WD}=\text{K}\Bigg[\frac{\text{V}^\frac{1}{2}}{\frac{1}{2}}\Bigg]^{\text{v}_2}_{\text{v}_1}=2\text{K}\big[\sqrt{\text{V}_{2}}-\sqrt{\text{V}_1}\big]$
WD form $\text{V}_1\text{to}\text{V}_2,\text{i.e},\text{dW}=2\text{P}_1\text{V}_1^\frac{1}{2}\big[\sqrt{\text{V}_2}-\sqrt{\text{V}_1}\big]$
$=2\text{P}_2\text{V}_2^\frac{1}{2}\big[\sqrt{\text{V}_2}-\sqrt{\text{V}_1}\big]$

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Question 42 Marks

If a refrigerator’s door is kept open, will the room become cool or hot? Explain.

Answer

If a refrigerator door is kept open the room will become hotter, because amount of heat absorbed from inside the refrigerator and work done on refrigerator by electricity both will be rejected by refrigerator in room.

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Question 52 Marks

Can a system be heated and its temperature remains constant?

Answer

If the system does work aganist the surrounding so that it compensates for the heat supplied, the tempreature can remain constant. It is given that $\Delta\text{T}=0\Rightarrow\Delta\text{U=0}$$\therefore\Delta\text{Q}=\Delta\text{U}+\Delta\text{W}$
$\Rightarrow\Delta\text{Q}=\Delta\text{W}$ so heat supplied to the system is utilized in expansion system is isothermal.

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Question 62 Marks

Air pressure in a car tyre increases during driving. Explain.

Answer

Volume of a car tyre is fixed. During driving, temperature of the gas increases while its volume remains constant. So, according to Charle’s law, at constant volume (V),
Pressure (P) $\propto$ Temperature (T)
Therefore, pressure of gas increases

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