State an expression, in terms of work done and heating, that is used to calculate the increase in internal energy of a system.

Question 5

(a) State an expression, in terms of work done and heating, that is used to calculate the increase in internal energy of a system. [2]

(b) State and explain, in terms of your expression in (a), the change, if any, in the internal energy

(i) of the water in an ice cube when the ice melts, at atmospheric pressure, to form a liquid without any change of temperature, [3]

(ii) of the gas in a tyre when the tyre bursts so that the gas suddenly increases in volume.

Assume that the gas is ideal. [3]

Reference: Past Exam Paper – November 2015 Paper 42 Q3

Solution:

(a)

{1^st law of thermodynamics:

ΔU = q + w

where  ΔU is the increase in internal energy of a system

q is thermal energy (heat) gained by the system

w is the work done on the system

Increase in internal energy = Heat supplied to system + Work done on system

We need to clearly specify the direction of energy changes.

Since the internal energy of the system increases, it should gain energy in terms of work done and heating.

By heating the system, it gains thermal energy (energy is transferred to the system by heating).

By doing work ON the system, it again gains energy. Note that if the system does work, it loses energy. (e.g. a person doing work means that the person is losing energy) So, work should be done ON the system} and NOT BY the system.

(b)

(i)

{ ΔU = q + w

Work w = pΔV            where ΔV is the change in volume

As ice melts into water, its volume decreases (this is a special case for ice – for the melting of other solids into liquids, the volume usually increases). So, work is done ON the system – this increases the internal energy. However, the change in volume from solid is liquid is very small, so the work done ON the system may be considered to be negligible. (w = positive or zero)

To change its state from solid to liquid, thermal energy is absorbed by water (ice) to break its lattice structure and change into a liquid. So, it again gains more energy. (Even if the temperature is not changing, energy is still required to change the state.) (q is positive)

So, the internal energy increases.}

(ii)

{As the gas expands, its volume increases. The gas needs to do work against the atmosphere to expand. So, it loses some of its energy. (w is negative)

The increase in volume occurs SUDDENLY. So, no thermal energy would enter or leave the system because the change takes place in a very short time. (q = 0)

So, the internal energy of the system decreases.}