Question

Jin knows that the initial internal energy of a closed system is 78 J and the final internal energy is 180 J. He also knows that 64 J of energy are used to do work. To find the heat added to the system, Jin completes the steps below.
1. Add the initial internal energy plus the final internal energy to find the change in internal energy.
2. Add the change in internal energy to the energy used to do work.
3. Write the answer in joules.

Which best describes Jin's error?

A )For step 1, he should have used 180 J as the change in internal energy.
B )For step 1, he should have subtracted 78 J from 180 J to find the change in internal energy.
C )For step 2, he should have subtracted the change in internal energy from the energy used to do work.
D )For step 2, he should have subtracted the energy used to do work from the change in internal energy.

Answer 1

As we know by the first law of thermodynamics

$Q = \Delta U + W$

here we know that

Q = heat given to the system

$\Delta U = U_f - U_i$

W = work done by the system

now here we can say

$\Delta U = 180 - 78 = 102 J$

$W = 64 J$

now we can say that heat will be given as

$Q = 64 + 102 = 166 J$

now here we can say that Jin does the error in his first step while calculation of change in internal energy as he had to subtract it while he added the two energy

So best describe Jin's Error is

B )For step 1, he should have subtracted 78 J from 180 J to find the change in internal energy.