# Heat is supplied uniformly at the rate of 100W to 1.0 × 10¯²kg of a…

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**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 ****× 10****²Jkg****¯¹K****¯¹**

**B. 2.0 ****× 10****²Jkg****¯¹**

**C. 4.0 ****× 10****⁴ Jkg****¯¹K****¯¹**

**D. 4.0 ****× 10****⁴ Jkg****¯¹**

**QUICK ANSWER…**

**C**

**DETAILS…**** **** **

**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…**

**Data given:**

**Power = 100w**

**Mass = 1.0 ****× 10****¯²kg**

**Time = 20s**

**Change in temperature = 5°c = 5K**

**FORMULA:**

**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) × 10****²**

**C = 400 × 10****²**

**C = 4 × 10****⁴**

**C = 4 × 10****⁴**** 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.**

**KEY-POINTS…**

**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 /**