Thermodynamis of air in a basketball

[amiv4]

Homework Statement

A player bounces a basketball on the floor, compressing it to 80.0 % of its original volume. The air (assume it is essentially N_2 gas) inside the ball is originally at a temperature of 20.0 C and a pressure of 2.00 atm. The ball's diameter is 23.9 cm

Temperature at maximum compression equals 47.4 C

By how much does the internal energy of the air change between the ball's original state and its maximum compression?
$$\Delta$$U=?

Homework Equations

$$\Delta$$U=nC_v$$\Delta$$T
C_v=20.76

The Attempt at a Solution

n=.0000058657

$$\Delta$$U=.00333657
but that's not right

 

[rock.freak667]

Start with the first law

Q-W=ΔU

now no heat is being added to the system so Q=0

You're left with ΔU= -W. What is the work done on the ball?

 

[amiv4]

W=nC_v(T_1-T_2)
that is the same thing i was using