Help please

Question

the pressure of a gas in a container varies directly with its temperature and inversely with its volume. At a temperature of 70 Kelvin and a volume of 10 cubic meters the pressure is 33.6 newtons per square meter. What is the pressure if the temperature is increased to 80 Kelvin and the volume is decreased to 6 cubic meters

Answer 1

Let P = pressure, T = temperature, and V = volume.  Since P varies directly with T and inversely with V:

 

P = k(T/V)

 

where k is the constant of proportionality.  Use the one data point given in the problem (T=70, V=10, P=33.6) to find k:

 

P = k(T/V)

PV/T = k

(33.6)(10)/(70) = k

4.8 = k

 

So the full equation is:

 

P = (4.8)(T/V)

 

For T = 80 Kelvin and V = 6 m³:

 

P = (4.8)(80/6)

P = 64 N/m²