Question

Based on the cyclic process shown in the graph, which point represents the coolest and hottest state of the gas? 

• A. Coolest-X, Hottest-Y
• B. Coolest-Y, Hottest-X
• C. Coolest-Y, Hottest-Z
• D. Coolest-Z, Hottest-Y

Hint:

Temperature is directly proportional to the product of Pressure and Volume.

Answer 1

The Correct Option is D

Step 1: Understand the goal.
A gas goes around a cyclic process shown on a pressure volume graph with points X, Y, and Z. We must find which point is coolest and which is hottest.

Step 2: Link temperature to P and V.
For an ideal gas, $PV = nRT$, so the temperature is proportional to the product $PV$. A higher $PV$ product means a hotter state.

Step 3: Decide the rule to apply.
So we simply compare the product of pressure and volume at each labelled point. The smallest product is the coolest point and the largest product is the hottest point.

Step 4: Find the coolest point.
Point Z sits at both low pressure and low volume, so its $PV$ product is the smallest. That makes Z the coolest state.

Step 5: Find the hottest point.
Point Y sits at high pressure together with a large volume, giving the biggest $PV$ product. That makes Y the hottest state.

Step 6: State the answer.
Coolest is Z and hottest is Y. \[ \boxed{\text{Coolest } Z, \ \text{Hottest } Y} \]