Question

When fuel is burned in a cylinder equipped with a piston, the volume expands from 0.265 Lto 1.390 Lagainst an external pressure of 1.01 atm In addition, 857 J is emitted as heat. What is ΔE for the burning of the fuel?

Answer 1

Answer:

Step 1: Explanation

According to the first law of thermodynamics the change in internal energy of a system (ΔU) equals to the net heat transfer into the system (Q)  plus the net work done on the system (W).

In equation form, the first law of thermodynamics is;

ΔE = Q + W

Where, ΔE = is the change in internal energy of the system.

Q =  is the net heat transferred into the system

W = is the net work done on the system.

Step 2: Calculate the work done

Given,

V1 = 0.265 L and V2 = 1.390 L and P ext = 1.01 atm

We know work done is given by

W = - P ext × ΔV

=> W = - P ext × ( V2-V1 ) = -1.01 atm  × ( 1.390 - 0.265 ) L = -1.13625 atm-L

Work done in Joules = (-1.13625 atm-L × 101.3 J / atm-L ) = -115.102125 J

Step 3: Calculation of internl energy

Given

Q = - 857 J [ here negative sign means heat is emitted from the system ]

w = -115.102125 J

By using the first law of thermodynamics

ΔE = Q + W

=>ΔE = (-857 J) + (-115.102125 J)

=> ΔE = -972.1 J

Hence, the ΔE of the burning of the fuel = -972.1 J