Question

（1）A 31.5-g glass thermometer reads 24.1 ∘C before it is placed in 139 mL of water. When the water and thermometer come to equilibrium, the thermometer reads 41.8 ∘C. Ignore the mass of fluid inside the glass thermometer. The value of specific heat for water is 4186 J/kg⋅C∘, and for glass is 840 J/kg⋅C∘. Part A What was the original temperature of the water?

（2）

A crate of fruit with a mass of 37.0 kgkg and a specific heat capacity of 3550 J/(kg⋅K)J/(kg⋅K) slides 8.00 mm down a ramp inclined at an angle of 40.0 degreesdegrees below the horizontal.

Part A If the crate was at rest at the top of the incline and has a speed of 2.25 m/sm/s at the bottom, how much work WfWf was done on the crate by friction? Use 9.81 m/s2m/s2 for the acceleration due to gravity and express your answer in joules.

（3）

The value of specific heat for copper is 390 J/kg⋅C∘J/kg⋅C∘, for aluminun is 900 J/kg⋅C∘J/kg⋅C∘, and for water is 4186 J/kg⋅C∘J/kg⋅C∘.

Part A What will be the equilibrium temperature when a 275 gg block of copper at 245 ∘C∘C is placed in a 155 gg aluminum calorimeter cup containing 865 gg of water at 14.0 ∘C∘C?

Answer 1

1) given
m_glass = 31.5 g = 0.0315 kg
m_water = 139 g (since 1 mL of water = 1 gram of water)
= 0.139 kg

Let T is the initial temperature of water

Heat lost by water = Heat gained by glass thermo meter

m_water*C_water*(T - 41.8) = m_glass*C_glass*(41.8 - 24.1)

0.139*4186*(T - 41.8) = 0.0315*840*(41.8 - 24.1)

==> T = 42.6 C <<<<<<<<-----------------Answer

2) vertical height of inclined path, h = 8*sin(40)

= 5.14 m

work done by friction on create = change in mechanical energy

= (1/2)*m*v^2 - m*g*h

= (1/2)*37*2.25^2 - 37*9.8*5.14

= -1770 J <<<<<<<<--------------------------Answer

3) let T will be equilibrium temperarure.

use, Heat lost by copper block = Heat gained by aluminum calorimeter

m_copper*C_copper*(245 - T) = m_aluminum*C_aluminum*(T - 14)

0.275*390*(245 - T) = 0.155*900*(T - 14)

==> T = 114.4 C <<<<<<<<<----------------------Answer