Pressure Volume diagram doubt

Question

In P-V graph of an ideal gas, there is a straight line with negative slope.

How can we calculate the maximum temperature from the graph?

Note:The graph is not a rectangular hyperbola but a straight line with negative slope.

Answer 1

Even though the temperature is changing, the equation of state of the ideal gas is still

 

PV = nRT

 

P = pressure

V = volume

n = number of moles

R = universal gas constant

T = absolute temperature

 

Since your straight line represents two extremes, evaluate PV at both extremes, then get the temperature, and see which one is higher.  Assuming the amount of gas is constant (n = constant),

 

T₁ = P₁V₁/(nR)

 

T₂ = P₂V₂/(nR)

 

The greater of T₁ or T₂ will be the maximum temperature.