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Question

The volume of an ideal gas enclosed in a thin, elastic membrane in a room at sea level where the air temperature is 18 °C is 8 x 10-3 m3. If the temperature of the room is increased by 17 °C, what is the new volume of the gas (in m3)? (Be careful about the unit of temperature in the equation.)

Answer 1

At both the initial and final conditions, the container with gas is in equilibrium with the local environment, and the initial and final pressures will be the same, which in this problem is sea level pressure. Therefore you can use the relation

V₁/T₁ = V₂/T₂

V₁ and T₁ are given.

T₂ = T₁ + 17^oC

You have sufficient information to solve for V₂. Be sure to first convert T₁ and T₂ to kelvins. V₁ is given in m³. Plug the numbers into

V₂ = (T₂/T₁) V₁

and get the final volume in m³.