A metal ball of mass 0.1 kg is heated upto 500°C and dropped into a vessel of heat capacity 800 JK^{−1} and containing 0.5 kg water. The initial temperature of water and vessel is 30°C. What is the approximate percentage increment in the temperature of the water? [Specific Heat Capacities of water and metal are, respectively, 4200 Jkg^{−1}K^{−1} and 400 Jkg^{−1}K^{−1}]

a. |
30% |
b. |
20% |

c. |
25% |
d. |
15% |

A metal ball of mass 0.1 kg is heated upto 500°C and dropped into a vessel of heat capacity 800 JK^{−1} and containing 0.5 kg water. The initial temperature of water and vessel is 30°C. What is the approximate percentage increment in the temperature of the water? [Specific Heat Capacities of water and metal are, respectively, 4200 Jkg^{−1}K^{−1} and 400 Jkg^{−1}K^{−1}]

a. |
30% |
b. |
20% |

c. |
25% |
d. |
15% |

1 Answer

127 votes

0.1 × 400 × (500 − T) = 0.5 × 4200 × (T − 30) + 800 (T − 30)

⇒ 40(500 − T) = (T − 30) (2100 + 800)

⇒20000 − 40T = 2900 T − 30 × 2900

⇒20000 + 30 × 2900 = T(2940)

T = 30.4°C

× 100 = × 100

= 20%

127 votes

127