Question

A certain mass of warm copper is brought into thermal contact with an equal mass of cooler lead. The copper loses 100.0 J of thermal energy as it cools and the lead gains the same energy by warming. Which metal has a greater magnitude of temperature change? Specific heat capacities:

Copper: 0.093 KCal/Kg.°C
Lead: 0.031 KCal/Kg.°C

Answer 1

Lead metal has a greater magnitude of temperature change.

Step-by-step explanation:

let the mass of copper and lead be m.

Energy loosed by Copper metal = -Q = -100 J

(Negative sign just indicates that energy is released)

Change in temperature warm of the copper =
`\Delta T`

Specific heat capacity of copper = c = 0.093 KCal/Kg°C = 389.112 J/kg°C

1 kCal = 4184 Joules

`Q=mc\Delta T`

`-100 J=m* 389.112 J/kg^oC* \Delta T`

`100=m* 389.112 J/kg^oC* \Delta T`

`\Delta T=(0.2569)/(m)`

Energy gained by lead metal = Q' = 100 J

Change in temperature lead=
`\Delta T'`

Specific heat capacity of lead = c' = 0.031 KCal/Kg°C = 129.704 J/kg°C

`Q=mc\Delta T`

`100 J=m* 129.704 J/kg^oC* \Delta T'`

`\Delta T'=(0.7709)/(m)`

On comparing temperature changes in both metals:

`(0.2569)/(m),(0.7709)/(m)`

`(0.2569)/(m)<(0.7709)/(m)`

`\Delta T<\Delta T'`

Lead metal has a greater magnitude of temperature change.