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Standard XII

Physics

Calorimetry

A calorimeter...

Question

A calorimeter has mass 100 g and specific heat 0.1 kcal/ kg $^{0}$ C. It contains 250 gm of liquid at $30^{0}$ C having specific heat of 0.4 kcal/kg $^{0}$ C. If we drop a piece of ice of mass 10 g at $0^{0}$ C. What will be the temperature of the mixture?

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Solution

$1 g = 7.716 C a l$
Implies,
$100 g = 771.6 c a l 771.6 / 1000 = 0.7716 k C a l$
$250 g = 1929 c a l = 1929 / 1000 = 1.929 k C a l$
$10 g = 77.16 c a l = 77.16 / 1000 = 0.07716 k C a l$
heat of fusion in ice(Latent) $= 80 k C a l / K g$
Heat lost in the process = (mass × heat capacity × change in temperature) -------→(i)
$(30 - T) \times 0.7716 \times 0.1 + (30 - T) 1.926 \times 0.4 = 0.07716 \times 80 + T \times 0.07716 \times 1$
$2.3148 - 0.07716 T + 23.112 - 0.7704 T = 6.1728 + 0.07716 T$
$2.3148 + 23.112 - 6.1728 = 0.07716 + 0.7704 + 0.07716$
$0.92472 \times T = 19.254$
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Q. Solve the following problems:
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A calorimeter has mass 100 g and specific heat 0.1 kcal/ kg $^{0}$ C. It contains 250 gm of liquid at $30^{0}$ C having specific heat of 0.4 kcal/kg $^{0}$ C. If we drop a piece of ice of mass 10 g at $0^{0}$ C. What will be the temperature of the mixture?