Answer:
Explanation:
The transitions occur as follows:
P₁ V₁ changes to 3P₁, V₁ (with constant volume) — first phase.
Subsequently, 3P₁,V₁ transitions to 3P₁, 5V₁ (with constant pressure) — second phase.
During the initial phase, the temperature must be escalated by a factor of 3. Therefore, if the starting temperature is T₁, then the ending temperature will be 3 T₁.
P₁V₁ = n R T₁, where n represents the number of moles of gas.
Thus, nRT₁ = P₁V₁.
The heat added at constant volume is given by n Cv (3T₁ - T₁),
= n x 5/3 R X 2T₁ (noting that for diatomic gas, Cv = 5/3 R).
= 10/3 x nRT₁
= 10/3 x P₁V₁.
In the second phase, the temperature must rise 5 times. Thus, if the initial temperature is 3T₁, then the final temperature will be 15 T₁.
The heat added at constant pressure in this scenario becomes:
= n Cp (15T₁ - 3T₁)
= n x 7/3 R X 12T₁ (for diatomic gases, Cp = 7/3 R).
= 28 x nRT₁
= 28 P₁V₁.
