# Question e69fc

Jun 14, 2016

$117.39 g$, rounded to two decimal places

#### Explanation:

We know that in such interactions heat is gained by one and is lost is by the other.

Also that the heat gained/lost is given by
$\Delta Q = m s t$ ....(1)
where $m , s \mathmr{and} t$ are the mass, specific heat and rise or gain in temperature of the object;
$\Delta {Q}_{\text{lost"=Delta Q_"gained}}$ .....(2)

In the given problem heat is lost by sample of copper and gained by water.

Heat gained by water to change its temperature from ${21.0}^{\circ} \text{C}$ to ${29.7}^{\circ} \text{C}$
$\Delta {Q}_{\text{gained}} = m s t$, Specific heat of water is 1calg^-1 "^@C^-1.
$\Delta {Q}_{\text{gained}} = 298 \times 1 \times \left(29.7 - 21.0\right)$
$\implies \Delta {Q}_{\text{gained}} = 2592.6 c a l$

Heat lost by the sample to change its temperature from $275.1 {.}^{\circ} \text{C}$ to ${29.7}^{\circ} \text{C}$, specific heat of copper=0.09calg^-1 "^@C^-1#. If ${m}_{s}$ is the mass of sample
$\Delta {Q}_{\text{lost}} = {m}_{s} \times 0.09 \times \left(275.1 - 29.7\right)$
$\implies \Delta {Q}_{\text{lost}} = 22.086 \times {m}_{s} c a l$

Using (2) we get

$22.086 \times {m}_{s} = 2592.6$
$\implies {m}_{s} = 117.39 g$, rounded to two decimal places
{"ft_lang_label":"__label__en","ft_lang_prob":0.8764353,"math_prob":0.99998164,"size":899,"snap":"2020-24-2020-29","text_gpt3_token_len":323,"char_repetition_ratio":0.13072626,"word_repetition_ratio":0.016129032,"special_character_ratio":0.38932148,"punctuation_ratio":0.16746412,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99999416,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-06-01T13:25:31Z\",\"WARC-Record-ID\":\"<urn:uuid:8b1d838f-12d6-4749-abfb-bfac360d5388>\",\"Content-Length\":\"34695\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b22b0e25-abc0-4289-a050-183d2a27cd95>\",\"WARC-Concurrent-To\":\"<urn:uuid:ec865c28-8f98-4c46-b808-2a2246634650>\",\"WARC-IP-Address\":\"216.239.32.21\",\"WARC-Target-URI\":\"https://socratic.org/questions/575f494f11ef6b5b281e69fc\",\"WARC-Payload-Digest\":\"sha1:NNE7QFWGHP7L26GOWWQVWB25RZXOBTR5\",\"WARC-Block-Digest\":\"sha1:RNJAHEJNFHGTYLPHB7MUHHVYOKUD42FQ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-24/CC-MAIN-2020-24_segments_1590347417746.33_warc_CC-MAIN-20200601113849-20200601143849-00169.warc.gz\"}"}