When 100g of liquid A at 100° C is added to 50g of liquid B at temperature 75° C , the final temperature of the mixture becomes 90° C . Similarly, if 100g of liquid A at 100° C is added to 50g of liquid B at 50° C , what will be the final temperature in ° C ?

Question

When 100g of liquid A at 100° C is added to 50g of liquid B at temperature 75° C , the final temperature of the mixture becomes 90° C . Similarly, if 100g of liquid A at 100° C is added to 50g of liquid B at 50° C , what will be the final temperature in ° C ? (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

In first case according to principle of calorimetry,
heat lost by liquid

A =

heat gained by liquid

B

∴ m_{A} c_{A} Δ T_{A} = m_{B} c_{B} Δ T_{B}

∴ 100 \times c_{A} (100 - 90) = 50 \times c_{B} (90 - 75)

∴ 1000 c_{A} = 50 \times 15 c_{B}

∴ 4 c_{A} = 3 c_{B} \dots . (i)

Similarly, in second case,

100 \times c_{A} (100 - T) = 50 \times c_{B} (T - 50)

∴ 4 c_{A} (100 - T) = 2 c_{B} (T - 50)

Using equation (i),

3 c_{B} (100 - T) = 2 c_{B} (T - 50)

∴ 300 - 3 T = 2 T - 100

∴ 5 T = 400

∴ T = 8 0^{\circ} C

Q. When 100g of liquid A at 100∘C is added to 50g of liquid B at temperature 75∘C , the final temperature of the mixture becomes 90∘C . Similarly, if 100g of liquid A at 100∘C is added to 50g of liquid B at 50∘C , what will be the final temperature in ∘C ?