The pressure in an automobile tire is 198 kpa at 300.0 k. at the end of a trip on a hot, sunny day, the pressure has risen to 225 kpa. what is the final temperature of the air in the tire, assuming the volume of the tire remains constant?
a. 149 k
b. 264 k
c. 322 k
d. 341 k

We can use the ideal gas equation which is expressed as PV = nRT. At a constant volume and number of moles of the gas the ratio of T and P is equal to some constant. At another set of condition, the constant is still the same. Calculations are as follows:

T1/P1 = T2/P2

T2 = P2 x T1 / P1

T2 = 225 x 300 / 198

T2 = 340.91 K

If the heat engine is a perfect carnot cycle engine, thenefficiency = (t2-t1)/t2   where t1=temperature of cold reservoir ( ° k) = 135            t2=temperature of hot reservoir ( ° k)   = 325thereforeefficiency = (t2-t1)/t2 = (325-135)/325 = 0.5846 = 58%  note: this is the theoretical maximum efficiency of a perfect heat engine.   real-life engines do not achieve this value.

Answersystem;