A container of hot liquid is placed in a freezer that is kept at a constant temperature of .The initial temperature of the liquid is After 3 minutes, the liquid's temperature is How much longer will it take for its temperature to decrease to Round your answer to
Two decimal places.
A)1.89 minutes
B)2.84 minutes
C)3.16 minutes
D)1.26 minutes
E)3.47 minutes

Question

A container of hot liquid is placed in a freezer that is kept at a constant temperature of  .The initial temperature of the liquid is  After 3 minutes, the liquid's temperature is  How much longer will it take for its temperature to decrease to  Round your answer to
Two decimal places.
A)1.89 minutes 
B)2.84 minutes 
C)3.16 minutes 
D)1.26 minutes 
E)3.47 minutes

Quizplus · Accepted Answer

To find the time it takes for the liquid to decrease from 11ebbd4d_3eec_0ab3_8a0a_4389ab7555ef_TB8202_11 to 11ebbd4d_3eec_0ab4_8a0a_ff8db197d331_TB8202_11, we need to find the temperature change per minute.

The temperature change in 3 minutes is:

11ebbd4d_3eec_0ab3_8a0a_4389ab7555ef_TB8202_11 - 11ebbd4d_3eec_0ab2_8a0a_41778ae77ec7_TB8202_11 = 11ebbd4d_3eec_0ab1_8a0a_a3bde1172394_TB8202_11

So the temperature change per minute is:

11ebbd4d_3eec_0ab1_8a0a_a3bde1172394_TB8202_11 / 3 = 11ebbd4d_3eec_0ab5_8a0a_19340c2eb676_TB8202_11

To find how long it takes for the temperature to decrease from 11ebbd4d_3eec_0ab3_8a0a_4389ab7555ef_TB8202_11 to 11ebbd4d_3eec_0ab4_8a0a_ff8db197d331_TB8202_11, we can use the formula:

(time needed) = (temperature change needed) / (temperature change per minute)

The temperature change needed is:

11ebbd4d_3eec_0ab3_8a0a_4389ab7555ef_TB8202_11 - 11ebbd4d_3eec_0ab4_8a0a_ff8db197d331_TB8202_11 = 11ebbd4d_3eec_0ab3_8a29_5c39ed5fe1f5_TB8202_11

So:

time needed = 11ebbd4d_3eec_0ab3_8a29_5c39ed5fe1f5_TB8202_11 / 11ebbd4d_3eec_0ab5_8a0a_19340c2eb676_TB8202_11 = 3.16

Rounding to two decimal places, we get 3.16 as the answer, which is choice C. To find out the time it takes for the liquid to cool from 11ebbd4d_3eec_0ab3_8a0a_4389ab7555ef_TB8202_11 to 11ebbd4d_3eec_0ab4_8a0a_ff8db197d331_TB8202_11, we need to know the rate at which it cools down. This is given by the temperature difference between the liquid and the freezer, which is constant at 11ebbd4d_3eec_0ab1_8a0a_a3bde1172394_TB8202_11.

The temperature difference between the initial temperature and the temperature after 3 minutes is:

11ebbd4d_3eec_0ab3_8a0a_4389ab7555ef_TB8202_11 - 11ebbd4d_3eec_0ab2_8a0a_41778ae77ec7_TB8202_11 = 11ebbd4d_3eec_0ab1_8a0a_a3dcb00afb50_TB8202_11

To cool down from 11ebbd4d_3eec_0ab3_8a0a_4389ab7555ef_TB8202_11 to 11ebbd4d_3eec_0ab4_8a0a_ff8db197d331_TB8202_11, we need to cool down by another:

11ebbd4d_3eec_0ab3_8a0a_4389ab7555ef_TB8202_11 - 11ebbd4d_3eec_0ab4_8a0a_ff8db197d331_TB8202_11 = 11ebbd4d_3eec_0ab1_8a0a_a3dcb00afb50_TB8202_11

So the total temperature difference is:

2 * (11ebbd4d_3eec_0ab1_8a0a_a3dcb00afb50_TB8202_11) = 11ebbd4d_3eec_0ab1_8a0a_a7b5d5e667a0_TB8202_11

Since the rate of cooling is constant, we can use the following formula to find out how long it will take to cool down by this amount:

time = (total temperature difference) / (rate of cooling)

time = 11ebbd4d_3eec_0ab1_8a0a_a7b5d5e667a0_TB8202_11 / 11ebbd4d_3eec_0ab1_8a0a_a3bde1172394_TB8202_11

time = 3.16 minutes

Rounding to two decimal places gives us choice C: 3.16 minutes.

A Container of Hot Liquid Is Placed in a Freezer