a) A cup of coffee takes 5 min. to drop from boiling to 120 F in a room that is
ID: 1422183 • Letter: A
Question
a) A cup of coffee takes 5 min. to drop from boiling to 120 F in a room that is 68 F. What is the temperature of the coffee after 20 min.? (b) A woman is waiting for her coffee for 7 minutes before walking up to the pick- up counter and asking why it’s taking so long. A barista reaches down and grabs a coffee and says, “I just finished up with it, here you go.” The woman takes it to a table outside and reads for 4 minutes before taking a sip. It’s cold. Maybe body temperature, she thinks. (You can use a rough estimate of body temperature.) Should she go back in and demand a new coffee because the barista lied, or does she only have herself to blame? Assume the room temperature is 68 F and it’s 85 F outside. (Assume the same decay constant (usually called k) as in the previous problem.)a) A cup of coffee takes 5 min. to drop from boiling to 120 F in a room that is 68 F. What is the temperature of the coffee after 20 min.? (b) A woman is waiting for her coffee for 7 minutes before walking up to the pick- up counter and asking why it’s taking so long. A barista reaches down and grabs a coffee and says, “I just finished up with it, here you go.” The woman takes it to a table outside and reads for 4 minutes before taking a sip. It’s cold. Maybe body temperature, she thinks. (You can use a rough estimate of body temperature.) Should she go back in and demand a new coffee because the barista lied, or does she only have herself to blame? Assume the room temperature is 68 F and it’s 85 F outside. (Assume the same decay constant (usually called k) as in the previous problem.)
a) A cup of coffee takes 5 min. to drop from boiling to 120 F in a room that is 68 F. What is the temperature of the coffee after 20 min.? (b) A woman is waiting for her coffee for 7 minutes before walking up to the pick- up counter and asking why it’s taking so long. A barista reaches down and grabs a coffee and says, “I just finished up with it, here you go.” The woman takes it to a table outside and reads for 4 minutes before taking a sip. It’s cold. Maybe body temperature, she thinks. (You can use a rough estimate of body temperature.) Should she go back in and demand a new coffee because the barista lied, or does she only have herself to blame? Assume the room temperature is 68 F and it’s 85 F outside. (Assume the same decay constant (usually called k) as in the previous problem.)
Explanation / Answer
(a) The temperature of coffee for 5 minutes, after it was dropped (120 0F).
using a formula to determine the value of "a" -
T0 = 120 (2)-at + 68
(120) = 120 (2)-5a + 68
(52) = 120 (2)-5a
(0.433) = 2-5a
(2)a = 1.182
a = 0.241
The temperature of the coffee after 20 min. which will be given as :
using an above formula, we have
T = 120 (2)-at + 68
T = 120 (2)-0.241 x 20 + 68
T = (120 / 24.82) + 68
T = (4.24 + 60) 0F
T = 72.2 0F
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