Question

A silver block, initially at 58.4∘C, is submerged into 100.0 g of water at 25.0∘C in an insulated container. The final temperature of the mixture upon reaching thermal equilibrium is 26.7∘C. The specific heat capacities for water and silver are Cs,water=4.18J/(g⋅∘C) and Cs,silver=0.235J/(g⋅∘C).

Answer 1

The mass of the silver block is 95.52 grams.

Step-by-step explanation:

Heat lost by silver will be equal to heat gained by the water

`-Q_1=Q_2`

Mass of silver=
`m_1`

Specific heat capacity of silver =
`c_1=0.235 J/g^oC`

Initial temperature of the silver =
`T_1=58.4^oC`

Final temperature of a silver =
`T_2=T=26.7^oC`=

`Q_1=m_1c_1* (T-T_1)`

Mass of water=
`m_1=100.0 g`

Specific heat capacity of water=
`c_2=4.186 J/g^oC`

Initial temperature of the water =
`T_3=25^oC`

Final temperature of water =
`T_3=T=26.7^oC`

`Q_2=m_2c_2* (T-T_3)`

`-Q_1=Q_2`

`-(m_1c_1* (T-T_1))=m_2c_2* (T-T_3)`

`-(m_1* 0.235 J/g^oC* (26.7^oC-58.4^oC))=100.0 g* 4.186 J/g^oC* (26.7^oC-25.0^oC)`

On substituting all values:

we get,
`m_1 = 95.52 g`

The mass of the silver block is 95.52 grams.