Heat is supplied uniformly at the rate of 100W to 1.0 × 10¯²kg of a…
Heat is supplied uniformly at the rate of 100W to 1.0 × 10¯²kg of a liquid for 20 seconds. If the temperature of the liquid rises by 5°C, then the specific heat capacity of the liquid is
A. 2.0 × 10²Jkg¯¹K¯¹
B. 2.0 × 10²Jkg¯¹
C. 4.0 × 10⁴ Jkg¯¹K¯¹
D. 4.0 × 10⁴ Jkg¯¹
First of all, you should quickly strike out options B and D.
This is because specific heat capacity is the quantity of heat energy needed to change the temperature of 1kg of a substance by 1 kelvin. Therefore, the right unit for specific heat capacity is Jkg¯¹K¯¹. let’s solve for the specific answer…
Power = 100w
Mass = 1.0 × 10¯²kg
Time = 20s
Change in temperature = 5°c = 5K
H = mcθ
Where H = heat supplied,
m = mass of the liquid,
c = specific heat capacity,
and θ = change in temperature
but if this heat is coming from an electric set up, with power consumed, then:
H = power × time = 100 × 20 = 2000J
Hence, substituting these into the first formula, we have:
H = mcθ
2000 = 1.0 × 10¯² × c × 5
2000 = 5 × 10¯² × c
C = 2000/(5 × 10¯²)
C = (2000/5) × 10²
C = 400 × 10²
C = 4 × 10⁴
C = 4 × 10⁴ Jkg¯¹K¯¹
Now for the right answer to the above question:
- A is not the right answer.
- B is incorrect. wrong unit.
- C is correct.
- D is incorrect. wrong unit.
You may please note this/these:
- The change in temperature did not change even as the unit changed from °c to K. this is because we are dealing with a net change and not a specific temperature.
- The unit of specific heat capacity is Jkg¯¹K¯¹ and not Jkg¯¹
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/ culled from 2020 JAMB-UTME physics past question 32 /