Question #89fac
1 Answer
Explanation:
You can answer this question without actually calculating the specific heats of the two substances.
As you know, a substance's specific heat tell you how much heat is needed in order to increase the temperature of
Notice that you're dealing with equal masses of substance
This means that the difference between the amount of heat needed to cause the same change in temperature for equal masses of both substances will reflect the difference in their specific heats.
More specifically, the substance that requires more heat to register the same change in temperature will have a higher specific heat.
In this case, substance
color(green)(|bar(ul(color(white)(a/a)color(black)(c_"B" = 2 xx c_"A")color(white)(a/a)|)))
To prove this result, you can calculate the two specific heats by using the equation
color(blue)(|bar(ul(color(white)(a/a)q = m * c * DeltaTcolor(white)(a/a)|)))" " , where
Convert the masses from kilograms to grams first
color(purple)(|bar(ul(color(white)(a/a)color(black)("1 kg" = 10^3"g")color(white)(a/a)|)))
Rearrange the equation to solve for
q = m * c * DeltaT implies c = q/(m * DeltaT)
Plug in your values to get
c_"A" = "500 J"/(5 * 10^3"g" * 2^@"C") = "0.05 J g"^(-1)""^@"C"^(-1)
c_"B" = "1000 J"/(5 * 10^3"g" * 2^@"C") = "0.1 J g"^(-1)""^@"C"^(-1)
As predicted, the specific heat of substance
color(green)(|bar(ul(color(white)(a/a)color(black)(c_"B" = 2 xx c_"A")color(white)(a/a)|)))