Question

A gas at \(800^{\circ} \mathrm{C}\) is cooled until both its pressure and volume are halved. The final temperature of the gas will be

• A. 473 K
• B. 373.25 K
• C. 293.29 K
• D. 268.25 K

Hint:

Convert to kelvin and use the combined gas law since the amount of gas is fixed.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
For a fixed amount of gas, \(\dfrac{PV}{T}\) is constant.

Step 2: Initial temperature
\(T_{1}=800+273=1073\ \text{K}\).

Step 3: Apply the law
\(\dfrac{P V}{T_{1}}=\dfrac{(P/2)(V/2)}{T_{2}}\Rightarrow T_{2}=\dfrac{T_{1}}{4}\).

Step 4: Calculation
\(T_{2}=\dfrac{1073}{4}=268.25\ \text{K}\).

Final Answer:
The final temperature is 268.25 K. \[ \boxed{\text{(D) }\text{268.25 K}} \]