a metallic sphere of mass 100 gram and at hundred degree celsius is dropped in a bucket full of water - Science - The Human Eye and the Colourful World

Question

a metallic sphere of mass 100 gram and at hundred degree celsius is
dropped in a bucket full of water weight of water is 1 5 kg and it
is a temperature of 15 degrees celsius what is the resulting
temperature of the system is that specific heat of the metallic
sphere is 1 3 into 10 raise to 3 joule per kg degree Celsius and
specific heat of water is 4 2 into 10 raise to 3 joule per kg
degree Celsius

Anshu Agrawal · Accepted Answer

Solution:
Mass of the metallic sphere (m1 )= 0
1 kg Initial temperature of the metallic sphere=1000C Final temperature=T0C Change in temperature (ΔT1 )= 100-T  Amount of heat lost by metallic sphere= m1×c1×ΔT1= 0
1kg×1
3×103×( 100-T )Mass of the water m2  =1
5 kg  Initial temperature of water = 150C Final temperature=T0C Change in temperature (ΔT2 )= T-15 Specific heat capacity of water (c2 )=4
2×103 Amount of heat gained by  water    = m2×c2×ΔT2    =1
5×4
2×103×T-15 At steady state, heat lost by metallic sphere= heat gained by waterTherefore 0
1kg×1 3×103×( 100-T )= 1 5×4
2×103×(T-15)∴ 0 13(100-T)=6 3(T-15)13-0
13T=6 3T-94 5107 5=6 43TT=16 710C