Three containers $$C1$$,$$C2$$ and $$C3$$ have water at different temperatures. The table below shows the final temperature T when different amounts of water (given$$ in $$liters) are taken from each container and mixed (assume$$ no loss of heat during the $$process)The$$ value of θ $$(in$$ $$0C$$ to the nearest $$integer) is $$-----------$$

Question

Three containers $$C1$$,$$C2$$ and $$C3$$ have water at different temperatures. The table below shows the final temperature T when different amounts of water (given$$ in $$liters) are taken from each container and mixed (assume$$ no loss of heat during the $$process)The$$ value of θ $$(in$$  $$0C$$  to the nearest $$integer) is $$-----------$$

Infinity Learn · Accepted Answer

First Mixing : $$1s$$ θ$$1$$−$$60+2s$$θ$$2$$−$$60+0s$$θ$$3$$−$$60=0$$​⇒θ$$1+2$$θ$$2=180$$  …………. $$1$$ Second Mixing : $$0s$$ θ$$1$$−$$30+1s$$θ$$2$$−$$30+2s$$θ$$3$$−$$30=0$$​⇒θ$$2+2$$θ$$3=90$$     …………. $$2$$ Third mixing : $$2s$$ θ$$1$$−$$60+0s$$θ$$2$$−$$60+1s$$θ$$3$$−$$60=0$$​⇒$$2$$θ$$1+$$θ$$3=180$$   …………. $$3$$ Solving equations $$1$$ $$2$$ and $$3$$ we get ​θ$$1=80$$, θ$$2=50$$, θ$$3=20$$ Fourth mixing : $$1s$$ θ$$1$$−θ$$+1s$$θ$$2$$−θ$$+1s$$θ$$3$$−θ$$=0$$ ⇒$$80$$−θ$$+50$$−θ$$+20$$−θ$$=0$$ ⇒θ$$=1503=50$$

Calorimetry

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