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Five-gram samples of copper and aluminum are at room temperature. Both receive equal amounts of energy due to heat flow. The specific heat capacity of copper is 0.09 cal/g°C, and the specific heat capacity of aluminum is 0.22 cal/g°C. Which of the following statements is true?

AThe temperature of each sample increases by the same amount.
BThe aluminum will get hotter than the copper.
CThe copper will get hotter than the aluminum.
DThe temperature of each sample decreases by the same amount

Verified Answer :

m₁ = mass of sample of copper = m₂ = mass of sample of aluminum = 5 g

T = initial temperature of copper = initial temperature of aluminum

T₁ = final temperature of copper

T₂ = final temperature of aluminum

c₁ = specific heat of copper = 0.09 cal/g°C

c₂ = specific heat of aluminum = 0.22 cal/g°C

Since both receive same amount of heat, hence

Q₁ = Q₂

m₁ c₁ (T₁ - T) = m₂ c₂ (T₂ - T)

(5) (0.09) (T₁ - T) = (5) (0.22) (T₂ - T)

T₁ - T = (2.44)  (T₂ - T)

Change in temperature of copper = (2.44) change in temperature of aluminum

hence the correct choice is

c. The copper will get hotter than the aluminum.

Answer: c. The copper will get hotter than the aluminum.

Explanation: Specific heat capacity of a substance is the amount of heat required to raise the temperature of 1 gram of water through \(1^0C\)

As we know that,  

\(Q=m\times c\times \Delta T\)

m= mass

c = specific heat

\(\Delta T\) = change in temperature

Given : \(Q_{Cu}=Q_{Al}\)

mass of copper = mass of Aluminium= 5 g

\(c_{Cu}\times \Delta T_{Cu}=c_{Al}\times \Delta T_{Al}\)      

Now put all the given values ,  we get

\(0.09\times \Delta T_{Cu}=0.22\times \Delta T_{Al}\)

Thus as specific heat capacity of copper is less, the temperature change will be more as they both are at same initial temperature.

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