Why use c_p and not c_v as specific heat - Thermodynamics

[yjl]

Hey all,

I am working on a problem that goes like this:

The cargo space of a refrigerated truck whose inner
dimensions are 12 m 3 2.3 m 3 3.5 m is to be precooled
from 25°C to an average temperature of 5°C. The construc-
tion of the truck is such that a transmission heat gain occurs
at a rate of 120 W/°C. If the ambient temperature is 25°C,
determine how long it will take for a system with a refrigera-
tion capacity of 11 kW to precool this truck.

The solutions manual calculates the mass of the air inside the truck and afterwards does
Q=mc_p\Delta T
to calculate the amount of heat removed.

My question is: why do we use c_p here and not c_v
It's a closed system, such that
Q=m(u_2-u_1)=mc_v\Delta T
right?

 

[BvU]

It's a closed system

How does the solution manual

The solutions manual calculates the mass of the air inside the truck

 

[rude man]

A truck is not really a closed system. It's much more liely to be vented somewhere to atmospheric pressure.