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Physics Question on thermal properties of matter

In an experiment on the specific heat of a metal, a 0.20 kg0.20\,kg block of the metal at 150∘150^\circC is dropped in a copper calorimeter (of water equivalent 0.025kg0.025 kg) containing 150 cm3150\,cm^3 of water at 27∘27^\circC. The final temperature is 40∘40^\circC. The specific heat of the metal is

A

344 kg−1C−1344\,kg^{-1}C^{-1}

B

434 kg−1C−1434\,kg^{-1}C^{-1}

C

234 kg−1C−1234\,kg^{-1}C^{-1}

D

332 kg−1C−1332\,kg^{-1}C^{-1}

Answer

434 kg−1C−1434\,kg^{-1}C^{-1}

Explanation

Solution

Here T1=150∘C, T2=27∘CT_1 = 150^\circ C, \, T_2 = 27^\circ C and T = 40∘C^\circ C ; M1=0.20 kg and w=0.025M_1=0.20 \,kg\,and\,w=0.025 Using heat gained = heat lost, we get (M2+w) C2(T−T2)=M1C1(T1−T)(150×10−3+0.025) (4.2×103)(40−20)(M_2 + w) \, C_2 ( T -T_2) = M_1 C_1 (T_1 - T) (150 \times 10^{-3} + 0.025) \, ( 4.2 \times 10^3) (40 - 20) = 0.20 C1_1 (150 - 40) or 9.555 ×103=22 C1\times 10^3 = 22 \, C_1 or C1C_1 = 434 J kg−1^{-1} C−1^{-1}