What is the temperature increase of the gas?

[Tori Grafe]

Homework Statement

In an empty rubber raft the pressure is approximately constant. You push on a large air pump that pushes 1.0L (1.0×10^−3 m^3) of air into the raft. You exert a 16N force while pushing the pump handle 2.0×10^−2 m .

Part A: Determine the work done on the gas.
Part B: If all of the work is converted to thermal energy of the 1.0 L of gas, what is the temperature increase of the gas? Assume that the air obeys the ideal gas law and is initially at 293 K.

2. Homework Equations
Just trying to come up with some equations that may help, although I have had no luck...
P*V=n*R*T
Work = -n*R*deltaT
W= (-/+) deltaP*V
Delta T = Q/c*m
U_thermal = 3/2*n*R*T
delta U = c*m*delta T

The Attempt at a Solution

Part A: I have already solved this part as you can see below...
Work = Force * Distance
Work = 16 N * 2.0x10^-2 m
Work = .32 N*m
Work = .32 (kg*m^2)/s^2
Work = .32 J

Part B: I have attempted a couple of times as you can see below... I really need help on this
Work = Q
Delta T = Q/c*m
m = ro * v
ro = 1.3 kg/m^3
v= 1.0x10^-3 m^3
c= 700 J/(kg * degrees C)
m = 1.3x10^-3 kg

delta T = .32J / (700 (J/(kg * degrees C)) * 1.3x10^-3 kg)

Work = -delta P * v
.32 J = -delta P * 1.0x10^-3
-delta P = 320 N/m^2
320 N/m^2 = n*R*delta T
320 N/m^2 = n*(8.314 J/mol * K)*delta T

 

[mooncrater]

I think the equation
ΔU=nC_vΔT
Might help you.