Question 566: Thermodynamics & KTG

Question

An insulated cylinder of volume $60 \mathrm{~cm}^3$ is filled with a gas at $27^{\circ} \mathrm{C}$ and 2 atmospheric pressure. Then the gas is compressed making the final volume as $20 \mathrm{~cm}^3$ while allowing the temperature to rise to $77^{\circ} \mathrm{C}$. The final pressure is $\_\_\_\_$ atmospheric pressure.

Accepted Answer

Initial state of the gas,
Initial Volume, $V_1=60 \mathrm{~cm}^3$
Initial Temperature, $\mathrm{T}_1=27^{\circ} \mathrm{C}=(27+273) \mathrm{K}=300 \mathrm{~K}$
Initial Pressure, $\mathrm{P}_1=2 \mathrm{~atm}$
Final state of the gas is,
Final Volume, $V_2=20 \mathrm{~cm}^3$
Final Temperature, $\mathrm{T}_2=77^{\circ} \mathrm{C}=(77+273) \mathrm{K}=350 \mathrm{~K}$
We need to calculate the pressure of the gas at final state.
Using Ideal gas equation, $\mathrm{PV}=\mathrm{nRT} \Rightarrow \frac{\mathrm{PV}}{\mathrm{T}}=\mathrm{nR}=$ constant
$$ \frac{\mathrm{P}_1 \mathrm{~V}_1}{\mathrm{~T}_1}=\frac{\mathrm{P}_2 \mathrm{~V}_2}{\mathrm{~T}_2} $$
$\Rightarrow \mathrm{P}_2=\frac{\mathrm{P}_1 \mathrm{~V}_1 \mathrm{~T}_2}{\mathrm{~T}_1 \mathrm{~V}_2}$
$$\Rightarrow $$ $P_2=\frac{2 	imes 60 	imes 350}{300 	imes 20} \mathrm{~atm}$
$$\Rightarrow $$ $\mathrm{P}_2=7 \mathrm{~atm}$

Thermodynamics & KTG

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