Question

A mass of gas at pressure P and temperature T (degrees Kelvin) and volume V satisfies the equation T = KPV where K is a constant. The initial temperature is 300 degrees Kelvin, the inital volume is 4 cubic centimeters, and the inital pressure is 4 [The units are N per square centimeter. This is force per unit area, which is what pressure is.] If the pressure increases by 7 % and the volume increases by 0.07 cubic centimeters, approximately how much does the temperature change by? [hint: use the initial information to find K]

Answer 1

The equation is T = KPV

Using the initial information you have, solve for K:

300 = K(4)(4)

Simplify:

300 = K(16)

Divide both sides by 16

K = 300/16

K = 18.75

Now if pressure increases by 7%, the new pressure would be 4 x 1.07 = 4.28

Volume increases by 0.07, so the new volume would be 4 + 0.07 = 4.07

Now solve for t:

T = 18.75(4.28)(4.07)

T = 326.6175

Now subtract the new temperature from the original one:

326.6175 - 300 = 26.6175 increase ( Round answer as needed).