Question

question 6 (1 point)
the relationship between heat transfer and change in temperature is given by q = mcδt, where c is specific heat capacity. under what conditions will c = q?
m = 1 kg δt = 1 °c
m = 1 g δt = 10 °c
m = 10 g δt = 10 °c
m = 100 g δt = 10 °c
m = 1 g δt = 1 °c

Explanation:

Step1: Rearrange the formula

Given \(Q = mc\Delta T\), we want to find when \(c = Q\). Rearranging the formula for \(c\) gives \(c=\frac{Q}{m\Delta T}\). If \(c = Q\), then \(\frac{Q}{m\Delta T}=Q\). Canceling \(Q\) (assuming \(Q
eq0\)), we get \(m\Delta T = 1\).

Step2: Check each option

• Option 1: \(m = 1\space kg=1000\space g\), \(\Delta T = 1^{\circ}C\). Then \(m\Delta T=1000\times1 = 1000

eq1\).

• Option 2: \(m = 1\space g\), \(\Delta T = 10^{\circ}C\). Then \(m\Delta T=1\times10 = 10

eq1\).

• Option 3: \(m = 10\space g\), \(\Delta T = 10^{\circ}C\). Then \(m\Delta T=10\times10 = 100

eq1\).

• Option 4: \(m = 100\space g\), \(\Delta T = 10^{\circ}C\). Then \(m\Delta T=100\times10 = 1000

eq1\).

• Option 5: \(m = 1\space g\), \(\Delta T = 1^{\circ}C\). Then \(m\Delta T=1\times1 = 1\).

Answer:

\(m = 1\space g\) and \(\Delta T = 1^{\circ}C\) (the fifth option).