How much does the temperature change by?

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 250 degrees Kelvin, the inital volume is 5 cubic centimeters, and the inital pressure is 6 [The units are N per square centimeter. This is force per unit area, which is what pressure is.]

 

If the pressure increases by 4 % and the volume increases by 0.08 cubic centimeters, approximately how much does the temperature change by? 

 

I've tried working this problem out, but keep getting marked wrong. Help would be greatly appreciated & writing out the steps is super helpful!

Answer 1

Ok, so the first step is going to be using all of the initial information to figure out what the constant 'k' is.  We start with the equation T = kPV and substitute in the given temperature, volume and pressure, then we can solve for 'k'.

 

We get:  250 = k(6)(5)

Simplified: 250 = 30k

Divide and solve for k: k = 25/3

 

So now we know k = 25/3.  Now lets use the extra information they give us to come up with the new equation.  They tell us the pressure increases by 4%.  The old pressure was 6, so we take 6 and multiply by 1.04 to get 6.24 -- so 6.24 is our new pressure.  They also tell us the volume increases by .08 cubic centimeters.  We started with 5 cubic centimeters, so we just add them together and get 5 + .08 = 5.08 cubic centimeters.  Now we substitute in everything we know:

 

Original equation: T = kPV

New equation: T = (25/3)(6.24)(5.08)

Simplify:  T = 264.16 degrees kelvin

 

So the new temperature is 264.16 degrees.  The old temperature was 250 degrees, so the temperature changed by 264.16 - 250 = 14.16 degrees kelvin.

 

I hope this helps!