Answer :
The specific heat of the block is 3349J/kg C if a 500 g block of an unknown substance in an insulated container.
We know very well that if a system is in equilibrium state, it means that Heat loss = Heat gained
Also, Quantity of heat gained or released is given by = mcΔ∅
where m is defined as mass of substance
c is defined as the specific heat capacity
and Δ∅ is defined as the change in temperature
Therefore, applying the above formula by assuming heat lost by water will be heat gained by the block.
=>m₁×c₁×(∅₂-∅₁) = m₂×c₂×(∅₁-∅₃)
where, we have m₂ as mass of water = 2kg
c₂ as specific heat capacity of water = 4186J/kg C
∅₃ as initial temperature of water = 20°C
Also, we have m₁ is defined as the mass of block = 500g = 0.5kg
c₁ is defined as the specific heat capacity of unknown substance
∅₂ is defined as block initial temperature = 50°C
∅₁ is defined as equilibrium temperature of block and water after mix= 25°C
Therefore, on putting the above quantities on above formula, we get
=>0.5×c₁×(50-25) = 2 x 4186×(25-20)
=>0.5×c₁×25=41860
=> c₁×12.5=41860
=>c₁=41860/12.5
=>c₁ = 3348.8J/kg C≅ 3349J/kg C
Hence, specific heat of the block is 3349J/kg C.
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