Question

A sample of gas inside a 150 mL piston has an initial temperature of 550 K and pressure of 9.9 atm. As the piston expands to 650 mL, the pressure decreases to 1.5 atm. What is the final temperature (in K) of the gas?

Remember that the ideal gas constant (R) has the same value for all gases, so P₁V₁/n₁T₁ = P₂V₂/n₂T₂. Also remember that the amount of gas remains constant in this problem (n₁ = n₂).

Select one:

a. 30 K

b. 361 K

c. 15730 K

d. 19 K

Answer 1

Given

initial gas pressure P₁ = 9.9 atm

initial gas volume V₁ = 150 ml

initial temperature T₁ = 550 K

Final pressure P₂ = 1.5 atm

final volume V₂ = 650 ml

lets assume final temperature = T₂

we know for an ideal gas

PV = nRT

or

Since R is a constant value we can write for intial and final conditions

and

Therefore

Since gas is present in a closed container we can assume n₁ = n₂

therefore

Hence

by substituting the given values T₂ = 1.5 x 650 x 550 / (9.9 x 150)

therefore T₂ = 361.1 K (or) T₂ = 361 K