FOLLOW US ON TWITTER
SHARE THIS PAGE ON FACEBOOK, TWITTER, WHATSAPP ... USING THE BUTTONS ON THE LEFT


YOUR PARTICIPATION FOR THE GROWTH OF PHYSICS REFERENCE BLOG

Tuesday, May 26, 2020

An ideal gas initially has pressure 1.0 × 105 Pa, volume 4.0 × 10-4 m3 and temperature 300 K, as illustrated in Fig. 2.1.


Question 5
An ideal gas initially has pressure 1.0 × 105 Pa, volume 4.0 × 10-4 m3 and temperature 300 K, as illustrated in Fig. 2.1.


Fig. 2.1

A change in energy of the gas of 240 J results in an increase of pressure to a final value of 5.0 × 105 Pa at constant volume.

The thermodynamic temperature becomes T.
(a) Calculate
(i) the temperature T, [2]

(ii) the amount of gas. [2]


(b) The increase in internal energy ΔU of a system may be represented by the expression
ΔU = q + w.

(i) State what is meant by the symbol
1. +q,
2. +w.
[2]

(ii) State, for the gas in (a), the value of
1. ΔU,
2. +q,
3. +w.
[3]
[Total: 9]





Reference: Past Exam Paper – November 2016 Paper 41 & 43 Q2





Solution:
(a)
(i)
{pV = nRT
The change occurs at constant temperature.
The amount of gas (number of moles) is also constant. R is the gas constant.
Taking into account the constant quantities,
p T
We can use proportion instead of finding each unknown quantity.}
p T               or pV / T = constant                or pV = nRT

{ p T
Initially, 1.0×105 300                        ------ (1)
After the change,   5.0×105 T         ------ (2)

Divide (2) by (1),
T/300 = (5.0×105)/(1.0×105)
T/300 = 5}

T (= 5 × 300 =) 1500 K


(ii)
pV = nRT

{We can use either the set of initial values of the quantities or the set of final values.}
{Set of initial values:}
1.0×105 × 4.0×10-4 = n × 8.31 × 300

or
{Set of final values:}
5.0×105 × 4.0×10-4 = n × 8.31 × 1500
n = 0.016 mol


(b)
(i)
1. +q: heating/thermal energy supplied
2. +w: work done on/to system

(ii)
1. ΔU = 240 J            {as given in the question}

2. +q = 240 J   {same value as given in 1. (= 240 J) and zero given for 3.}
{ΔU = q + w
+240 = q + 0
+q = +240 J}

3. +w = zero
{Since there is no change in volume,
+w = pΔV = 0}

No comments:

Post a Comment

If it's a past exam question, do not include links to the paper. Only the reference.
Comments will only be published after moderation

Currently Viewing: Physics Reference | An ideal gas initially has pressure 1.0 × 105 Pa, volume 4.0 × 10-4 m3 and temperature 300 K, as illustrated in Fig. 2.1.